Something is wrong with the sound board: when I turn the volume up, the game resets immediately. If the volume is low, I can play for couple of minutes, then the game resets. If I disconnect the sound board, the game works fine...

I don't know pinball boards, but it does sound like overload protection kicking in, maybe the amp is overheating and tripping the overload, that is, if there is an overload protector on the boards somewhere, the power board, etc.
And it could be the overload protector itself is faulty, or a bad capacitor, transistor or diode.

Problem solved! I posted my problem on five forums, and read the extensive Data East repair guide on www.pinrepair.com.
I changed the rectifier bridge on power supply board, and changed burnt or warped connectors: two large square molex connectors, and one 9-pin connector in the upper right corner. Tommy now works fine, no more resets. Thanks to all who tried to help!